1. limx->0 (cos(x)-1)/sin(2x)
I have it down to (-sinx^2)/((sin2x)(1+cosx)), but I can't seem to finish it
2. For my second question I don't even have a start. Here it is.
limx->0 (ln(1+x)/(sin3x))
Thank you so much in advance
$\displaystyle \lim_{x \to 0} \frac{ln(1+x)}{\sin 3x}=\lim_{x \to 0} \left ( \frac{ln(1+x)}{\sin 3x} \cdot \frac{3x}{3x} \right ) $
$\displaystyle = \lim_{x \to 0} \left ( \frac{ln(1+x)}{ 3x} \cdot \frac{3x}{\sin 3x} \right ) $
$\displaystyle =\frac{1}{3} \lim_{x \to 0} \left (\frac{ln(1+x)}{ x} \right ) \cdot \lim_{x \to 0} \left (\frac{1}{\frac{\sin 3x}{3x}} \right ) $
$\displaystyle =\frac{1}{3} \cdot 1 \cdot 1 = \frac{1}{3}$